What is the approximate value of a local maximum for the polynomial?

Solution: 

We need to calculate at least the second derivative of a polynomial, to know about the maxima or minima of the function.

If the second derivative of the function is zero, then there is no maxima or minima at that point in the curve.

To find the local maximum of a polynomial, we need to find the slope of the points where its value is zero.

f '(x) = 0

Let this value correspond to the point x = x₀ on the polynomial curve.

Now we need to check for the local maximum, by applying the following condition on the second derivative of the function.

f ''(x) at ( x = x₀ ) should be less than zero so to form a local maxima at x = x₀

      ( Representation of Global maxima in a graph)

Thus, f ''(x₀) < 0 is the condition for all values of x = x₀, where the polynomial will have a local maximum.

What is the approximate value of a local maximum for the polynomial?

Summary:

f ''(x₀) < 0 is the condition for all values of x = x₀, where the polynomial will have a local maximum.